Nuij type pencils of hyperbolic polynomials

Krzysztof Kurdyka, Laurentiu Paunescu

Nuij's theorem states that if a polynomial $p\in \mathbb{R}[z]$ is hyperbolic (i.e., has only real roots) then $p+s{p}^{\prime }$ is also hyperbolic for any $s\in \mathbb{R}$. We study other…